J. Hori (Niigata University, Japan)
B. He (University of Illinois at Chicago, USA)
In the present paper, spatial filters for inverse estimation of an equivalent dipole layer from the scalp-recorded potentials have been explored for their suitability in achieving high-resolution electroencephalogram (EEG) imaging.
It is of importance and interesting to image brain electrical activity from noninvasive electrical measurements on the scalp. However, the spatial resolution of conventional EEG is limited due to the smearing effect caused by the head volume conductor. Moreover, as the measurement electrode number is always much smaller than the dimension of the unknown dipole layer vector, this problem is an underdetermined non-unique inverse problem.
Spatial enhancement, which attempts to deconvolve the low-pass spatial filtering effect of volume conduction in the head, is one of the approaches to overcome such difficulty. In particular, cortical dipole imaging technique, which attempts to estimate the cortical potentials from scalp potentials through an intermediate source layer, have an advantage that no ad hoc information about the nature of sources is required.
In the present study, we consider the influence of non-uniform additive noise, which is characterized by noise covariance. We have applied the parametric projection filter (PPF), which uses the information of noise covariance, to perform the inverse regularization in cortical dipole imaging, and examined the feasibility of these spatial filters in a volume-conductor head model.
In a clinical situation, the noise information may be estimated from data that is known to be source free, such as pre-stimulus data in evoked potentials. We applied above restoration methods to the inverse problem in the conditions of various noises, such as Gaussian white noise (GWN) and non-uniform noise to simulate noise-contaminated scalp potential measurements.
The present results suggest that the PPF are effective for the condition of low correlation between signal and noise and that have similar restorative ability to the general inverse with truncated singular value decomposition and the Tikhonov regularization method for the GWN and the condition of high correlation between signal and noise. Further investigation using experimental data is necessary to fully validate the performance of PPF for cortical dipole imaging.
PIERS Progress In Electromagnetic Research Symposium in 2002, p. 595, Cambridge, July 2002 (invited).
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